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Intuition

I was looking at blogs on google and I found one that referrred to an article I once wrote on how to get a job in finance. The blog quoted something I wrote about the importance of gaining intuition:

“And, importantly, seek to gain intuition. Quantitative finance isnít mathematics or chess; itís not a field for brilliant idiot savants; itís an attempt to model the world of markets and people, and you need a little wisdom and experience to know what can work.”

Then, the blogger added a coda:

“There’s not much there about how to “gain intuition” though, so good luck with that. While you are at it, you might try gaining super-powers and esp too.”

It’s a good point. In the course I teach on the vol smile at Columbia, I try hard to somehow get the intuition about the various models across to the students, rather than mathematics. But I never thought about how to systematically do that. Here are some random thoughts. I’m sure other people have other suggestions.

– Look for interesting results in papers, or in observations; then try to “derive” them qualitatively.

– Or see if you can derive the same results with much simpler mathematics.

– Or, better, first try to think about it qualitatively, and then check your reasoning with the math.

– Many papers obscure the simplicity of their approach with complex and formal mathematics. Try to see what the essence of the paper is, in terms of assumptions and methodoloty, and then see if you can get to the result yourself, qualitatively, in pictures. – Think about extreme cases where you know the answer (e.g. deep in the money, deep out) because it’s obvious, then try to move a liittle away from them.

– Try to internalize the mathematics and its results in order to go one level higher.

– Use simple pictorial methods to understand how to tackle something. (That’s why I like the binomial model.)

As a personal example, my colleagues and I once noticed that in the computed results of local vol models the slope of the implied vol was about half the slope of the local vol at-the-money. We thought that was interesting and then found a way to derive that approximately. Then, that half reminded us of the similar relation between yield to maturity and forward rates. In that way we got to think about implied vol as an average over local vols. That proved to be a fruitful and often accurate way to think about the model.

Next blog session I will tackle how to get super-powers.

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